An Introduction to Nonlinear Solid Mechanics

Lecturer: prof. Anna M. Pandolfi (Politecnico di Milano)

Timetable:  6 - 16 November 2023

Schedule: see the attachment. The course is held online for UniTrento students, and in presence at PoliMI.

Overview. Rigorous introduction to nonlinear solid mechanics, especially addressing finite kinematics, material frame
indifference, constitutive models within a thermodynamic framework. Analysis of nonlinear material behaviors.

Specific topics:
1. Mathematical preliminaries. Dual basis. Tensors.
2. Kinematics of deformations. Motions, kinematics of local deformation. Polar decomposition.
3. Conservation laws (mass, linear & angular momentum, energy). Thermodynamics. Virtual work principle.
4. Constitutive theories. Coleman-Noll’s theory. Material frame indifference. Thermodynamic potentials. Kinetic
relations. Material classification.
5. Hyperelasticity. Elasticity symmetry. Internal constraints. Elastic materials: isotropic, transversally isotropic,
anisotropic materials.
6. Finite Plasticity. Multiplicative decomposition of the deformation gradient. Exponential and logarithmic mapping.
J2 plasticity. Pressure dependent plasticity.
7. Special materials: fiber reinforced tissues, liquid crystals.

TEACHING ORGANIZATION
• The course, 5 credits for the Italian learning system, is delivered online in 7 lectures of 4 hours each, using drawing
tablet and slides. Most lectures deal with theoretical explanations and proofs, supported by examples and
applications. Lecture notes are provided. Standard textbooks in continuum mechanics and exercise material are
suggested for further readings in each specific topic.
• Learning evaluation: theoretical exam on the whole program, by appointment (Only for the Trento University and
Politecnico di Milano students). 

Duration: 28 hours (5 credits)

Registration: in order to register for the course please send an email to dicamphd [at] unitn.it